It may come from a visual impression, much the same way a "charlie-foxtrot" brings images of arms and legs and sweaty bodies all intertwined. "Man! That was a real cluster-fuck!" Maybe roping a goat is a chaotic thing?

When I was in high school a "goat roper" was one of the students from an agricultural family and who looked the part. ("Load-os" were the druggies and "jocks" were still jocks.)

Over on the Phrase Finder discussion boards, the same question was asked, with a few people chiming in with Slang Dictionary definitions. The explanation I like the best is that "goatrope" comes from "goatrape" or "goatfuck", which is like a "clusterfuck". As with most slang, the exact etymology seems a little hazy.

Harder than it looks. Calves, those come out of the chute straight and start running. Goats, well, they'll stop right there and jump, or they'll try to climb into the stands, or try to eat the barrels. Not that I've ever tried it myself, but where I grew up in Northern California, the two big social events of the season were the county fair and the rodeo. They also featured " mutton-bustin' ", which was kids from five to ten who tried to ride sheep for at least ten seconds.

Doing some further looking today after reading some of these posts, I ran across the following from www.saddlemule.com

Goat Tying- Entry Fee $15.00.......... Donor: Southworth Catering, (307) 548-[....] Cross the starting line, run to the goat, throw and tie any three legs, time ends when goat tying string is released from both hands. Goat must stay tied for 6 seconds. 10 second penalty for runner over goat or goat rope.

All you get is 10 seconds for running over the goat? Man, sucks to be the goat.

Lighter(RHDHAS) can cite it first in print from 1968-79 in Current Slang "An agricultural student. New Mexico State."

Now, this of course just indicates a marker for appearing in print in English. So, it would not be unreasonable to assume it was used in speech, almost certainly out West, in the 10 years or so before that.

He indicates that the usage indicated "an unsophisticated rustic."

I'm gonna suggest that it was Western slang that migrated to VietNam with US troops and became the goatfuck, etc. indicating "fucked up.".

"Goat roper" was high school slang for a farm kid in Fayetteville, Arkansas, ca. 1980. For as long as I can recall, I've heard "goat roping" and "goat rodeo" used to mean a chaotic situation in which every party seems to be going in a different direction. Note that among speakers from whom I've heard this usage, there's a fine nuance of distinction from "clusterfuck", which describes a chaotic situation in which there are way too many parties involved, each of which feels compelled to make a contribution to an apparently shared common goal. Thus, in a goat rodeo, no one knows what's supposed to be happening so everyone's doing something different, while in a clusterfuck everyone agrees on what's supposed to happen, but everyone's trying to do it in their own way, all at once.

You city folks obviously have never been to a "Lil' Britches" or youth rodeo. Nowadays it is a little bit more organized but just a generation ago a "goat rope" or "goat roping" was a vision of confusion but great fun to watch.

Basically a herd of goats and a bunch of little kids (as in youthful cowboys) with ropes and on foot would be released at the same time and the assignment was for a pair of the budding Monty Montanas to lasso and tie a goat. Goats were run over, fellow ropers were lassoed, kids were knocked down and at times angry goats would take after the supposed two-legged agressor.

These days it's a lot more organized, there are a number of different events that involve goat roping and tying.

A side note here: last year I gave myself the assignment of covering the national championships for chicken roping. Now that is weird.